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Full text of "History Of The Theory Of Numbers - I"

XIX. IT Rxnr ^ %• ,%i\* n \nr\ ^ »,
A  !   M n.-MML-.j ,^';i, *. • ,. *   * ,      -«r   »'' -- i/^IWetiyt ^4»;,r<k >!. t fit t<> !r    -1     if '   .* ^ tr-i'. t    f     »i-%i»^.              >1,
/  / ,                                 r   *
7---,-;>'• *-'*••.'-- = - Ł--•
H'» i^uiU w*i »Aprrv«'»i 1,4 r^' ^ fc- *;» nn' f mi "f/' ^L^^kr"4 ,iLtl            la
< Laj ttr X    N^ ai- § L Mti"*- '.• **%!; / i^ka
R. IiH?f4 mi4 proved tint, il F *'  *-2f i , rnler^ '; ^r^c? ,>ve" all the
i" «r? ^f «\
wfc^re tin ^uxmuati^r * exterd r >\r «'J tLe <» .m1 iiritl -:*! 2, 3,      at a cf iLe di-tiiiit prn*e fai't«T- i, f.         ; <f   .    Thy rrm * f.»L'jW<          a
di-trihLti'T* of nil the fuctc.re ;f ?}' into tw*i       > *& I F.   PL. all the of n in! > ^et <S, all di^or?«f r. »2 hit* • ?e. 7". */J i ff   ; in.-( F, etc,, all divi-«r r^ i,f ^    ^   into »S, all of r.   * :  K.o x\ et'\* a1! f f ?     :"*" *  into !F, etc. TL».L, »vith the exception of ^ itself, every cHrl-cr i*». c.r^rf a5 ^ften in the rtt S as in the set F.   In particular. f-r Euler'* «p *. , ^=2o *i . ^^i    vr]
p 77* • — ^.     - c "*"**c5            ""
For                            see Dedekkd*1 of Ch. VIII.                   Fim) =
Il/.cf)
J. Liouville*            siinultanecj<ly with Dedekind the
for                          the same application to o ^ •
Liouville* stated the theorem for sums as a pr?Kein.
:Jcur. fur 51ath., 9, 1S32, 105; Werke, 4, 591.    He wn?t< 3m for ,». n;.
SJ^ , 4S, 1&54, 301-316.
•Observatioiiefl quaedam in             numerorum, Berlin, IS3Q; pp. 3-6,
«Jc-ur. fur Math., 54, 1S57. pp. 21, 25.
sJeur de                            ;2j, 2, 1S57, 110-2,
•Ncuv. Ana. Math,, 16, 1S57, 1S1-2.
441